The study on active safety motion control of automobiles is not only of great significance to the protection of people's lives and properties, but also of great significance to the development of unmanned driving technology under extreme conditions. Drifting maneuver suggests that the vehicle remains controllable when tires are at high slip conditions. Therefore, the research of drift control is helpful to achieve the active safety motion control of automobiles under extreme conditions. This paper focuses the steady drifting control with safety boundary constraints. The nonlinear 3-DOF vehicle model, the energy phase plane, the yaw acceleration isoclines, and sideslip rate isoclines are used to define the safety boundaries for steady drifting. ILQR algorithm are used for steady drifting control with safety boundary constraints. The simulation results suggests controller can better limit the yaw rate within the constraint boundary, compared with the controller without state boundary constraints.